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The theory of irreversible thermodynamics is applied to derive governing equations for history-dependent diffusion in polymers and polymer matrix composites from first principles. A special form for Gibbs free energy is introduced using stress, temperatures, and moisture concentration as independent state variables. The resulting governing equations are capable of modeling the effect of interactions between complex stress, temperature, and moisture histories on the diffusion process within an orthotropic material. Since the mathematically complex nature of the governing equations precludes a closed-form solution, a variational formulation is used to derive the weak form of the nonlinear governing equations which are then solved using the finite element method. For model validation, the model predictions are compared with published experimental data for the special case of isothermal diffusion in an unstressed Graphite-Epoxy symmetric angle-ply laminate.
non-Fickian, anomalous, diffusion, entropy, polymers, composites, two-stage, finite-element, modeling
Assistant Professor, University of Missouri-Rolla, Rolla, MO